Inertial coupling has been known since around 1948 [1]. It is essentially a gyroscopic effect, occurring in high roll-rate maneuvers of modern high-speed airplanes including spinning missiles designed in such a way that most of their masses are concentrated in the fuselage. For such an airplane, a slight deviation of its control surface angle from the steady-state angle may lead to a drastic change in roll-rate, causing damage on its empennage; known as the jump phenomenon. Nonlinear analyses to elucidate this problem have been reported in [2, 3], for example. However, the airplanes treated in these works are stable around the equilibrium point of level flight. On the other hand, an intrinsically unstable reentry vehicle, if combined with a malfunction of its AFCSs, may result in a catastrophe once it falls into a high roll-rate motion.

This does sound an awful lot like what happened to both of DARPA’s HTV-2 vehicles. Departure from controlled flight due to inertia coupling was the cause of a loss of crew in the early X-2 testing [4].

Simple explanations are usually not the reason for flight test accidents or mishaps. Experience has shown that there is usually a chain of events that lead to the mishap. Day gives a great summary of the combination of contributing factors that lead to the fatal X-2 test [4],

Optimum energy boost trajectory.

The rocket burn was longer than predicted by 15 sec and positioned the pilot further from Muroc Dry Lake than expected.

Decrease in directional stability as speed increased.

Decrease in directional stability with increased lift, leading to a reduced critical roll rate for inertial coupling.

Adverse aileron control (control reversal).

High positive effective dihedral.

Rudder locked supersonically.

Mass properties in window of susceptibility for inertial roll coupling.

Day describes the result of hitting an unstable region in the control parameter space:

At low-speeds this might be recoverable, but it is simply intractable to design a hypersonic aircraft to handle the loads this kind of rapid motion imposes on the vehicle structure. Eventually something gives, and this “jump” leads rapidly to catastrophic failure.

Day summarizes the reasoning for not modifying the X-2 for manned hypersonic flight,

The X-2 was unfortunately in the twilight zone of progress where rocket power, structural integrity, and thermodynamics were sufficiently advanced to push the aircraft to supersonic speeds. However, hydraulic controls and computerized control augmentation systems were not yet developed enough to contend with the instabilities.

And a relevant snippet from the more recent bifurcation analysis,

If it has unstable dynamics in the neighborhood of a trim point, a slight external disturbance or a slight deviation of control surface angles from their precise values at the trim point cannot allow the vehicle to stay at the trim point [5].

The flight regime that HTV-2 is operating in is unknown enough that it is difficult for designers to know before flight if the flight profile will put the vehicle into an unstable region of the control space. I thought the language that the program manager (a fellow AFIT alum btw) used to describe the post-flight analysis was interesting,

“Assumptions about Mach 20 hypersonic flight were made from physics-based computational models and simulations, wind tunnel testing, and data collected from HTV-2s first test flight the first real data available in this flight regime at Mach 20,” said Air Force Maj. Chris Schulz, HTV-2 program manager who holds a doctorate in aerospace engineering. “Its time to conduct another flight test to validate our assumptions and gain further insight into extremely high Mach regimes that we cannot fully replicate on the ground.” DARPA Press Release

I've noticed physics-based is a common meme for climate policy alarmists trying to shore-up the credibility of simulation predictions. There’s that same tone of, “The Science Says...”, which leads to unwarranted confidence in a situation of profound ignorance (unquantifiable uncertainty). I’ve also observed that program managers seem to take great comfort in the aura of a model that is “physics-based” as a talisman against criticism (“just look at these colorful fluid dynamics, you must be really stupid to question Physics…”). Of course, “physics-based” can be said of all sorts of models of varying fidelity. It is a vague enough moniker to be of great political or rhetorical use. Not that I think Schulz is one of these shady operatives since he goes on to say,

“we wouldn't know exactly what to expect based solely on the snapshots provided in ground testing. Only flight testing reveals the harsh and uncertain reality.”

As DARPA has been well informed by recent experience, ignorance becomes apparent only when confronted with the reality of interest. “Physics-based” is no guarantee of predictive capability.

4 comments:

Day on "control coupling" (my emphasis): Because this phenomenon had not previously been encountered, no identifying label, such as inertial coupling or dutch roll, existed. The phenomenon was simply referred to as the control parameter. Eighteen years later, Rockwell engineers using wind-tunnel data rediscovered that this instability would occur during the Space Shuttle entry and solved the problem by use of reaction rockets and a sophisticated computer control system; neither of which was available during the X-2 program.

The fixes used by the Rockwell engineers sound quite similar to the fixes DARPA implemented after the first HTV-2 flight test (I imagine they were already using a "sophisticated computer control", my emphasis): For its second test flight, engineers adjusted the vehicle’s center of gravity, decreased the angle of attack flown, and will use the onboard reaction control system to augment the vehicle flaps to maintain stability during flight operations.Hypersonic Aircraft Ready for Launch

"Filling the gaps in our understanding of hypersonic flight in this demanding regime requires that we be willing to fly." --Regina Duncan, DARPA

“According to a preliminary review of the data collected prior to the anomaly encountered by the HTV-2 during its second test flight,” said DARPA Director Regina Dugan, “HTV-2 demonstrated stable aerodynamically controlled Mach 20 hypersonic flight for approximately three minutes. It appears that the engineering changes put into place following the vehicle’s first flight test in April 2010 were effective. We do not yet know the cause of the anomaly for Flight 2.”

A detailed analysis conducted by an independent Engineering Review Board following the first flight test, prompted engineers to adjust the vehicle’s center of gravity, decrease the angle of attack flown and use the onboard reaction control systems to augment vehicle flaps during the vehicle’s second flight test. Those changes appear to have been effective. “An initial assessment indicates,” said Schulz, “that the Flight 2 anomaly is unrelated to the Flight 1 anomaly.”DARPA PR

Aerodynamic assumptions and extrapolations from known flight regimes proved inadequate when preparing for HTV-2 inaugural flight test. The data from second flight revealed that extrapolating from known flight regimes and relying solely on advanced thermal modeling and ground testing could not successfully predict the harsh realities of Mach 20 atmospheric flight. Engineering Review Board Concludes Review of HTV-2 Second Test Flight

Speaking at the American Institute of Aeronautics and Astronautics Joint Propulsion Conference earlier this week, Bowers said, “The first X-51 was mostly a success, the second flight was a hung store [failed to release from the B-2 mothership] and on the third the inlet started but un-started. Every flight test we’ve had has been a learning opportunity, and until we took it to flight we really didn’t know the unknowns.”Third X-51A Hypersonic Test Targeted For Mid-August